calculus 2 (find area and volume)

hi can you guys help me?

1. Find the area between the curves:
y=x^3–10x^2+24x
and y=–x^3+10x^2–24x

2. You wake up one morning, and find yourself wearing a toga and scarab ring. Always a logical person, you conclude that you must have become an Egyptian pharoah. You decide to honor yourself with a pyramid of your own design. You decide it should have height h=830 and a square base with side s=870

3. Find the volume of the solid formed by rotating the region enclosed by

x=0 x=1 y=0 y=8+x^4 about the x-axis.

4. A ball of radius 11 has a round hole of radius 3 drilled through its center. Find the volume of the resulting solid

5. Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by
y=x^4
y=27x
about the x-axis.

get the intersection points or graph them both to find them, if you graph them check which function is higher and integrate that one minus the other one in the range of the intersection points...

if you don't graph the functions, then after you get the intersection points (equal one function to the other and solve for x), evaluate both functions somewhere inside the intersection points and whichever functions gets a larger value it's higher...

i did it quickly and the intersection points are: at 0, 4 and 6

if you graph them you'll notice how they behave, if not, check again for which function is higher between the second set of intersection points...